This invention proposes a handling-switching apparatus including a number of conveyor tables, each constituted by a rotating carpet on which the piece to be handled is placed and that performs unloading into collecting vessels that are determined at the moment of introducing the piece into the machine, said collecting vessels being placed along the path below the carpets. A handling-switching apparatus of this kind is already known from the Italian Patent Application No. MI91A2213 dated Jun. 6, 1991, of the same applicant.